Poyet, who took charge of the Spanish club in the summer, was subjected to chants from the Betis supporters at the end of the Real Madrid clash, but the club's vice-president has given the Uruguayan a vote of confidence.
"Yes, we fully support the coach. We're eight league games in, we have eight points and we haven't found the game we want yet," Lopez Catalan told Movistar+. "It's something that Gustavo also recognises, but we must continue working so we can reach our [desired] results.
"It's normal for the beticos to be upset, we're all very upset. The fans didn't deserve it. We've built a new team, with 12 signings and a new coach, and this is something that takes time to bear fruit. We have to keep working."
Next up for Betis is a trip to fellow strugglers Osasuna on Friday night.